Home
Class 12
MATHS
The chance of defective screws in three ...

The chance of defective screws in three boxes `A ,B ,Ca r e1//5,1//6,1//7,` respectively. A box is selected at random and a screw draw in from it at random is found to be defective. Then find the probability that it came from box `Adot`

Text Solution

Verified by Experts

Let `E_(1),E_(2),and E_(3)` denote the events of selecting boxes A,B,C, respectively and A be the event that a screw selected at random is defecitive. Then,
`P(E_(1))=P(E_(2))=P(E_(3))=1//3`
`thereforeP(A//E_(1))=1/5,P(A//E_(2))=1/6,P(A//E_(3))=1/7`
By Bayes's rule, the required probability is
`(P(E_(1))P(A//E_(1)))/(P(E_(1))P(A//E_(1))+P(E_(2))+(A//E_(2))+P(E_(3))P(A//E_(3)))`
`=(1/3xx1/5)/(1/3xx1/5+1/3xx1/6+1/3xx1/7)=42/107`
Promotional Banner

Similar Questions

Explore conceptually related problems

There are N+1 identical boxes each containing N wall clocks.r^(th) box contains (r-1) defective and (N-r+1) effective clocks for 1<=r<=N+1. A box is selected at random and from this box a clock is chosen at random and is found to be effective,the probability that it is from km box is (2N2k+lambda)/(N^(2)+N) then find lambda .

(for explantion of Baye's rule ) three boxes contain 6 red , 4 black , 5 red , 5 black and 4 red , 6 black balls repectively one of the box is selected at random and a ball is drawn from it . If the ball drawn is red , find probability that it is drawn from the first bag .

A box contains 90 discs,numbered from 1 to 90. If one disc is drawn at random from the box,find the probability that it bears a prime number <23 .

There are two boxes containing 5 white and 6 blue balls and 3 white and 7 blue balls respectively.If one of the boxes is selected at random and a ball is drawn from it,then the probability that the ball is blue is